JEE Main 2021 — Parabola Question with Solution
From: JEE Main 2021 (Online) 17th March Evening Shift
Question
Let L be a tangent line to the parabola y2 = 4x 20 at (6, 2). If L is also a tangent to the ellipse , then the value of b is equal to :
Choose an option
Show full solutionCorrect option: B
Correct answer
B14
Step-by-step explanation
Parabola y2 = 4x 20
Tangent at P(6, 2) will be
2y = 2x + 12 20
2y = 2x 8
y = x 4
x y 4 = 0 ....... (1)
This is also tangent to ellipse
Apply c2 = a2m2 + b2
(4)2 = (2)(1) + b
b = 14
Tangent at P(6, 2) will be
2y = 2x + 12 20
2y = 2x 8
y = x 4
x y 4 = 0 ....... (1)
This is also tangent to ellipse
Apply c2 = a2m2 + b2
(4)2 = (2)(1) + b
b = 14
Practice this on the real CBT interface
Solve this JEE Main question (and the rest of the Parabola chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.
Solve interactively →About this question
This is a previous-year question from JEE Main 2021, covering the Parabola chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.